Block #554,554

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/20/2014, 11:24:51 PM · Difficulty 10.9626 · 6,252,581 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

01a1779a33892c22636205eb7ef321aeb02a65bd2f28aa191f00d821d7f1a40b

View on Chainz ↗

Height

#554,554

Difficulty

10.962590

Transactions

Size

662 B

Version

Bits

0af66c45

Nonce

263,419,615

Timestamp

5/20/2014, 11:24:51 PM

Confirmations

6,252,581

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

4d7ffe23a47234d71556ea5937be4e0bd3b8a6123a38d970be9f3b7435cbf8f7

Transactions (3)

Coinbaseba3e10b3d03eba…1259b2dd6c8e6b

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

38981cafaeede7…6b15a5a8e62880

1 in → 2 out3.5782 XPM227 B

AVGCGSyH…sk4xkioD AJPSj4aY…V9S9Bt73

2f7de86f4fcc03…39d3a067919015

1 in → 2 out4.9448 XPM226 B

AZLfPj22…wvLjkP9A AWEm1NVx…BSyUpTdF

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.

2.861 × 10¹⁰²(103-digit number)

28611331168399884076…14458646356783923199

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

2.861 × 10¹⁰²(103-digit number)

28611331168399884076…14458646356783923199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.861 × 10¹⁰²(103-digit number)

28611331168399884076…14458646356783923201

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

5.722 × 10¹⁰²(103-digit number)

57222662336799768152…28917292713567846399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.722 × 10¹⁰²(103-digit number)

57222662336799768152…28917292713567846401

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

1.144 × 10¹⁰³(104-digit number)

11444532467359953630…57834585427135692799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.144 × 10¹⁰³(104-digit number)

11444532467359953630…57834585427135692801

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

2.288 × 10¹⁰³(104-digit number)

22889064934719907261…15669170854271385599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.288 × 10¹⁰³(104-digit number)

22889064934719907261…15669170854271385601

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

4.577 × 10¹⁰³(104-digit number)

45778129869439814522…31338341708542771199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.577 × 10¹⁰³(104-digit number)

45778129869439814522…31338341708542771201

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

9.155 × 10¹⁰³(104-digit number)

91556259738879629044…62676683417085542399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #554,554

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