Block #315,946

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/16/2013, 7:10:20 PM · Difficulty 10.1197 · 6,476,827 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aabcb1fa07bcc3d48839e8a341f9b42f356b7432adc3c4c8527f20dc57de387c

View on Chainz ↗

Height

#315,946

Difficulty

10.119672

Transactions

Size

1.65 KB

Version

Bits

0a1ea2d7

Nonce

38,609

Timestamp

12/16/2013, 7:10:20 PM

Confirmations

6,476,827

Merkle Root

274b1bb091e6e81785a04bd54f49fb6a35244e9d102e88ed47fab4ce4e904ba3

Transactions (4)

Coinbase09d32cd9dfacb6…c8ae5f9daeddda

1 in → 25 out9.7500 XPM913 B

Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AMiJebLB…rK2iN8iS Ad9pSzHt…cpJ3y2zz AKEwr54i…9BfmMkRh

a1e893ee5193a4…49e2630a55cac5

1 in → 2 out9.9800 XPM227 B

AJvXN2ZZ…DEVkNad7 AawsHqKM…hrqBgDsN

8c6ffbb1fb56ba…4b071cc4a5b046

1 in → 2 out9.9800 XPM226 B

ARvxBB3H…hPMRo2z9 Aanuioj7…1SaJdqfb

615e077afdde1e…0b8775b1184841

1 in → 2 out8.9645 XPM226 B

AY6K6EvY…aGwc66od AY6dYxAs…FBirbevW

Prime Chain Origin

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

1.097 × 10¹⁰⁶(107-digit number)

10978857104273967564…84526393459810406399

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

1.097 × 10¹⁰⁶(107-digit number)

10978857104273967564…84526393459810406399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.097 × 10¹⁰⁶(107-digit number)

10978857104273967564…84526393459810406401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

2.195 × 10¹⁰⁶(107-digit number)

21957714208547935128…69052786919620812799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.195 × 10¹⁰⁶(107-digit number)

21957714208547935128…69052786919620812801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

4.391 × 10¹⁰⁶(107-digit number)

43915428417095870256…38105573839241625599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.391 × 10¹⁰⁶(107-digit number)

43915428417095870256…38105573839241625601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

8.783 × 10¹⁰⁶(107-digit number)

87830856834191740513…76211147678483251199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.783 × 10¹⁰⁶(107-digit number)

87830856834191740513…76211147678483251201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.756 × 10¹⁰⁷(108-digit number)

17566171366838348102…52422295356966502399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.756 × 10¹⁰⁷(108-digit number)

17566171366838348102…52422295356966502401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer