Block #558,615

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/23/2014, 4:13:22 PM · Difficulty 10.9640 · 6,244,434 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a96c6a2625795208ee3d40ced1df01cc31c12f1802cb43bfb309fa21e1fd2d21

View on Chainz ↗

Height

#558,615

Difficulty

10.963964

Transactions

Size

1.51 KB

Version

Bits

0af6c650

Nonce

398,198,216

Timestamp

5/23/2014, 4:13:22 PM

Confirmations

6,244,434

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a2a69d3b7e91f503ad60e084c726fbc7ec8cfcac711f7a3f02a040605a0b4923

Transactions (3)

Coinbase513476716c27ee…8788117dd775b6

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

09c072db4097d5…46854cce3c20bb

1 in → 2 out8.3000 XPM226 B

ANBppBRT…p4BVWf5k AMH2M1td…wVdRjb37

299d7456152a72…52fb85ea173b1a

7 in → 2 out50.2594 XPM1.08 KB

AJkNM1Md…xYoDMjF3 AHBBr72K…zttecnSG

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.

6.875 × 10⁹⁸(99-digit number)

68757668061124196961…93745079963734801919

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

6.875 × 10⁹⁸(99-digit number)

68757668061124196961…93745079963734801919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.875 × 10⁹⁸(99-digit number)

68757668061124196961…93745079963734801921

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

1.375 × 10⁹⁹(100-digit number)

13751533612224839392…87490159927469603839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.375 × 10⁹⁹(100-digit number)

13751533612224839392…87490159927469603841

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

2.750 × 10⁹⁹(100-digit number)

27503067224449678784…74980319854939207679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.750 × 10⁹⁹(100-digit number)

27503067224449678784…74980319854939207681

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

5.500 × 10⁹⁹(100-digit number)

55006134448899357568…49960639709878415359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.500 × 10⁹⁹(100-digit number)

55006134448899357568…49960639709878415361

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

1.100 × 10¹⁰⁰(101-digit number)

11001226889779871513…99921279419756830719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.100 × 10¹⁰⁰(101-digit number)

11001226889779871513…99921279419756830721

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