Block #317,594

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/17/2013, 7:34:16 PM · Difficulty 10.1517 · 6,491,504 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b6c146ffef9223f4e6948aa93b2940426eafa6ba82b581d5cb67568977033220

View on Chainz ↗

Height

#317,594

Difficulty

10.151677

Transactions

Size

1.02 KB

Version

Bits

0a26d451

Nonce

200,862

Timestamp

12/17/2013, 7:34:16 PM

Confirmations

6,491,504

Mined by

⛏️ aRrAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

e41e343a77cb8f48e941dcb563d96aa00c67c57c99b9cf25ab889d4f11a01130

Transactions (1)

Coinbasee41e343a77cb8f…889d4f11a01130

1 in → 26 out9.6866 XPM947 B

Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 Ad9pSzHt…cpJ3y2zz APeshfYV…3PKcKMKH APsPtagS…ismQazQb

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.

9.905 × 10¹⁰⁰(101-digit number)

99053119130471025639…83740531501532211199

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

9.905 × 10¹⁰⁰(101-digit number)

99053119130471025639…83740531501532211199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.905 × 10¹⁰⁰(101-digit number)

99053119130471025639…83740531501532211201

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

1.981 × 10¹⁰¹(102-digit number)

19810623826094205127…67481063003064422399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.981 × 10¹⁰¹(102-digit number)

19810623826094205127…67481063003064422401

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

3.962 × 10¹⁰¹(102-digit number)

39621247652188410255…34962126006128844799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.962 × 10¹⁰¹(102-digit number)

39621247652188410255…34962126006128844801

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

7.924 × 10¹⁰¹(102-digit number)

79242495304376820511…69924252012257689599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.924 × 10¹⁰¹(102-digit number)

79242495304376820511…69924252012257689601

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

1.584 × 10¹⁰²(103-digit number)

15848499060875364102…39848504024515379199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.584 × 10¹⁰²(103-digit number)

15848499060875364102…39848504024515379201

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

Block #317,594

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