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Block #1,371,757

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2015, 5:19:59 PM Β· Difficulty 10.8109 Β· 5,472,980 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cfc6e74e0518d2ceaa2c9c9d514eb700043da4c3a15153f0862d2bd9d1e82d0a
View on Chainz β†—

Height

#1,371,757

Difficulty

10.810900

Transactions

1

Size

243 B

Version

2

Bits

0acf9722

Nonce

562,191,223

Timestamp

12/16/2015, 5:19:59 PM

Confirmations

5,472,980

Mined by

⛏️ P2SHAbNVgXWJCnXJ31RnMLH7T3xjBzg3uNfMnj

Merkle Root

95ee3c5e310153fe10f0994d0655fe1b1b64adaf0b7fcba0e85bff92af3d2fac
Transactions (1)
Coinbase95ee3c5e310153…5bff92af3d2fac
1 in β†’ 2 out8.5400 XPM152 B
AbNVgXWJ…g3uNfMnjALPu3s2c…EJXLjVFh
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.

4.234 Γ— 10⁹⁢(97-digit number)
42343197600506415308…50800253492844216319
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
4.234 Γ— 10⁹⁢(97-digit number)
42343197600506415308…50800253492844216319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.234 Γ— 10⁹⁢(97-digit number)
42343197600506415308…50800253492844216321
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
8.468 Γ— 10⁹⁢(97-digit number)
84686395201012830616…01600506985688432639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.468 Γ— 10⁹⁢(97-digit number)
84686395201012830616…01600506985688432641
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
1.693 Γ— 10⁹⁷(98-digit number)
16937279040202566123…03201013971376865279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.693 Γ— 10⁹⁷(98-digit number)
16937279040202566123…03201013971376865281
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
3.387 Γ— 10⁹⁷(98-digit number)
33874558080405132246…06402027942753730559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.387 Γ— 10⁹⁷(98-digit number)
33874558080405132246…06402027942753730561
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
6.774 Γ— 10⁹⁷(98-digit number)
67749116160810264493…12804055885507461119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.774 Γ— 10⁹⁷(98-digit number)
67749116160810264493…12804055885507461121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:58,002,307 XPMΒ·at block #6,844,736 Β· updates every 60s
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