Block #554,130

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/20/2014, 2:55:27 PM · Difficulty 10.9632 · 6,244,805 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

293e4e17ea4fe705ff1e6b6b00e9a8f7295ac6a74e1983a3c95e7b648d407487

View on Chainz ↗

Height

#554,130

Difficulty

10.963193

Transactions

Size

852 B

Version

Bits

0af693cf

Nonce

190,465,667

Timestamp

5/20/2014, 2:55:27 PM

Confirmations

6,244,805

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1fdd4e9160bb227ada1741627545d9715a9ed6a4bbd5a204305447affbf355de

Transactions (4)

Coinbase340053ed7426b9…4bc9f7617108e3

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

0fa1739da885ae…377bb39596d020

1 in → 2 out8.3200 XPM191 B

AeKNrjNj…1NEq95Ta AULrA6RB…uzZHijMz

c2dfe1c125b783…85b3d0b541f012

1 in → 2 out7.7868 XPM226 B

AGdWVjRk…LFVsqCnK AdjKyU45…u3MLxRgK

6b682ab798da0a…ad6135b425af19

1 in → 2 out6.1228 XPM226 B

AZNVNP7M…7q4zcbyL ATTj3Quj…RogtXXPS

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.

4.984 × 10¹⁰⁰(101-digit number)

49841417956542663615…61333966298956625919

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

4.984 × 10¹⁰⁰(101-digit number)

49841417956542663615…61333966298956625919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.984 × 10¹⁰⁰(101-digit number)

49841417956542663615…61333966298956625921

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

9.968 × 10¹⁰⁰(101-digit number)

99682835913085327231…22667932597913251839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.968 × 10¹⁰⁰(101-digit number)

99682835913085327231…22667932597913251841

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

1.993 × 10¹⁰¹(102-digit number)

19936567182617065446…45335865195826503679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.993 × 10¹⁰¹(102-digit number)

19936567182617065446…45335865195826503681

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

3.987 × 10¹⁰¹(102-digit number)

39873134365234130892…90671730391653007359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.987 × 10¹⁰¹(102-digit number)

39873134365234130892…90671730391653007361

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

7.974 × 10¹⁰¹(102-digit number)

79746268730468261784…81343460783306014719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.974 × 10¹⁰¹(102-digit number)

79746268730468261784…81343460783306014721

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