Block #679,900

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/16/2014, 7:42:27 AM · Difficulty 10.9629 · 6,119,247 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6bf2cc81b062adeb07fb6b14e09a85d587dd10a2a8204de54378bc331e14e959

View on Chainz ↗

Height

#679,900

Difficulty

10.962870

Transactions

Size

1001 B

Version

Bits

0af67ea8

Nonce

110,088,447

Timestamp

8/16/2014, 7:42:27 AM

Confirmations

6,119,247

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

cbfe1f7355db07543e05f22d27774b4a253626b5b4d316324c04baaf7e1b2859

Transactions (4)

Coinbasec245ae837db3e2…d8579fb35f0692

1 in → 1 out8.3403 XPM116 B

ANSXnLY2…Sd25TjkD

663d2210eb33f9…e8cd97a12274d0

2 in → 1 out1.5100 XPM341 B

AdX1TZ55…uMJ4wnv5

9986e4cc915c0a…a4cb8555b2dc31

1 in → 2 out7.2318 XPM226 B

ALSq37KF…tuQSSZMJ ANxCbvRN…8Vg4CFTA

2c2a28ae602410…38e068a8122937

1 in → 2 out2.1627 XPM227 B

AWp1Hp5K…tYGjPL6S ATgAgYKV…vJbELgd3

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.

2.977 × 10⁹⁷(98-digit number)

29779536091636249096…83627619778441195519

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

2.977 × 10⁹⁷(98-digit number)

29779536091636249096…83627619778441195519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.977 × 10⁹⁷(98-digit number)

29779536091636249096…83627619778441195521

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

5.955 × 10⁹⁷(98-digit number)

59559072183272498192…67255239556882391039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.955 × 10⁹⁷(98-digit number)

59559072183272498192…67255239556882391041

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

1.191 × 10⁹⁸(99-digit number)

11911814436654499638…34510479113764782079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.191 × 10⁹⁸(99-digit number)

11911814436654499638…34510479113764782081

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

2.382 × 10⁹⁸(99-digit number)

23823628873308999277…69020958227529564159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.382 × 10⁹⁸(99-digit number)

23823628873308999277…69020958227529564161

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

4.764 × 10⁹⁸(99-digit number)

47647257746617998554…38041916455059128319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.764 × 10⁹⁸(99-digit number)

47647257746617998554…38041916455059128321

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