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Block #2,718,777

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 6/24/2018, 3:54:21 AM Β· Difficulty 11.6131 Β· 4,126,393 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
daa027afde0999c6407aeab36fdf392013337aee9642c9d722b37a898156738b
View on Chainz β†—

Height

#2,718,777

Difficulty

11.613145

Transactions

1

Size

201 B

Version

2

Bits

0b9cf70a

Nonce

284,911,053

Timestamp

6/24/2018, 3:54:21 AM

Confirmations

4,126,393

Mined by

⛏️ P2SHAVXM6FURivGmv29JyrYfMuLVraBame8Bui

Merkle Root

a305c0a463e3dc8202831924f61a4a1e99b1455928fef83652ed1db86fc74a21
Transactions (1)
Coinbasea305c0a463e3dc…ed1db86fc74a21
1 in β†’ 1 out7.4000 XPM110 B
AVXM6FUR…Bame8Bui
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.853 Γ— 10⁹⁢(97-digit number)
28531460153678902822…16517393244833710079
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
2.853 Γ— 10⁹⁢(97-digit number)
28531460153678902822…16517393244833710079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.853 Γ— 10⁹⁢(97-digit number)
28531460153678902822…16517393244833710081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
5.706 Γ— 10⁹⁢(97-digit number)
57062920307357805645…33034786489667420159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.706 Γ— 10⁹⁢(97-digit number)
57062920307357805645…33034786489667420161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.141 Γ— 10⁹⁷(98-digit number)
11412584061471561129…66069572979334840319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.141 Γ— 10⁹⁷(98-digit number)
11412584061471561129…66069572979334840321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
2.282 Γ— 10⁹⁷(98-digit number)
22825168122943122258…32139145958669680639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.282 Γ— 10⁹⁷(98-digit number)
22825168122943122258…32139145958669680641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
4.565 Γ— 10⁹⁷(98-digit number)
45650336245886244516…64278291917339361279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.565 Γ— 10⁹⁷(98-digit number)
45650336245886244516…64278291917339361281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
9.130 Γ— 10⁹⁷(98-digit number)
91300672491772489032…28556583834678722559
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
9.130 Γ— 10⁹⁷(98-digit number)
91300672491772489032…28556583834678722561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜…β˜†
Rarity
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:58,005,791 XPMΒ·at block #6,845,169 Β· updates every 60s
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