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Block #2,715,466

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/21/2018, 8:58:56 PM Β· Difficulty 11.6117 Β· 4,125,016 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d70d184c1807df3286163bb4441e4ebcb12904386939abbfd7f837aed8d9c1ab
View on Chainz β†—

Height

#2,715,466

Difficulty

11.611736

Transactions

1

Size

200 B

Version

2

Bits

0b9c9ac1

Nonce

1,788,181,091

Timestamp

6/21/2018, 8:58:56 PM

Confirmations

4,125,016

Mined by

⛏️ P2SHAGABAmuN9twfL9i6Lmko8E92G7MZ8SkCEQ

Merkle Root

c6deb4e8ff13d95af8f797c0f2772b8278519c6782b5a5c8cf686eef9396b8c9
Transactions (1)
Coinbasec6deb4e8ff13d9…686eef9396b8c9
1 in β†’ 1 out7.4000 XPM109 B
AGABAmuN…MZ8SkCEQ
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.

9.760 Γ— 10⁹⁡(96-digit number)
97604697243890938640…45738166415971953919
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
9.760 Γ— 10⁹⁡(96-digit number)
97604697243890938640…45738166415971953919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.760 Γ— 10⁹⁡(96-digit number)
97604697243890938640…45738166415971953921
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
1.952 Γ— 10⁹⁢(97-digit number)
19520939448778187728…91476332831943907839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.952 Γ— 10⁹⁢(97-digit number)
19520939448778187728…91476332831943907841
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
3.904 Γ— 10⁹⁢(97-digit number)
39041878897556375456…82952665663887815679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.904 Γ— 10⁹⁢(97-digit number)
39041878897556375456…82952665663887815681
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
7.808 Γ— 10⁹⁢(97-digit number)
78083757795112750912…65905331327775631359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.808 Γ— 10⁹⁢(97-digit number)
78083757795112750912…65905331327775631361
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
1.561 Γ— 10⁹⁷(98-digit number)
15616751559022550182…31810662655551262719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.561 Γ— 10⁹⁷(98-digit number)
15616751559022550182…31810662655551262721
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
3.123 Γ— 10⁹⁷(98-digit number)
31233503118045100365…63621325311102525439
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:57,968,186 XPMΒ·at block #6,840,481 Β· updates every 60s
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