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Block #2,701,438

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/11/2018, 10:56:51 PM Β· Difficulty 11.6304 Β· 4,114,844 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6326556fdf4da0df7278edb2913936943d6fa6f5cd0685fc8d4d036a4b8ec52e
View on Chainz β†—

Height

#2,701,438

Difficulty

11.630439

Transactions

2

Size

869 B

Version

2

Bits

0ba1646b

Nonce

1,089,594,772

Timestamp

6/11/2018, 10:56:51 PM

Confirmations

4,114,844

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

ec8f8e64470fa230fdadfa84b18de15e995f265479f6f1bc582242d9651c8689
Transactions (2)
Coinbase9dacbdbb0667a6…313b13db373c08
1 in β†’ 1 out7.3900 XPM110 B
AZtxQr2F…7grUWrUz
8b43cabc52fd7c…13985fd734b5ed
4 in β†’ 2 out267.5977 XPM668 B
Aa6dnmN8…7x6t92HsAaCt2Z2e…QB2Doko7
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.

2.005 Γ— 10⁹⁷(98-digit number)
20053309660905306506…08892832827171307519
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
2.005 Γ— 10⁹⁷(98-digit number)
20053309660905306506…08892832827171307519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.005 Γ— 10⁹⁷(98-digit number)
20053309660905306506…08892832827171307521
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
4.010 Γ— 10⁹⁷(98-digit number)
40106619321810613012…17785665654342615039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.010 Γ— 10⁹⁷(98-digit number)
40106619321810613012…17785665654342615041
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
8.021 Γ— 10⁹⁷(98-digit number)
80213238643621226024…35571331308685230079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.021 Γ— 10⁹⁷(98-digit number)
80213238643621226024…35571331308685230081
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
1.604 Γ— 10⁹⁸(99-digit number)
16042647728724245204…71142662617370460159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.604 Γ— 10⁹⁸(99-digit number)
16042647728724245204…71142662617370460161
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
3.208 Γ— 10⁹⁸(99-digit number)
32085295457448490409…42285325234740920319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.208 Γ— 10⁹⁸(99-digit number)
32085295457448490409…42285325234740920321
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
6.417 Γ— 10⁹⁸(99-digit number)
64170590914896980819…84570650469481840639
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,774,372 XPMΒ·at block #6,816,281 Β· updates every 60s
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