Block #504,080

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/21/2014, 1:30:10 PM · Difficulty 10.8078 · 6,306,344 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

628904e374309b80ed41101504cf774900b3f81750319ed0f9f37c254e9eb9cf

View on Chainz ↗

Height

#504,080

Difficulty

10.807814

Transactions

Size

1.15 KB

Version

Bits

0acecce3

Nonce

1,214,326,983

Timestamp

4/21/2014, 1:30:10 PM

Confirmations

6,306,344

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

e925e2769e4bfa8954b358aa22261b0d22110c2b3a79f9465e2d52c0db6999c6

Transactions (4)

Coinbase7da44f9ee72021…9b7faa46b3f68a

1 in → 1 out8.5800 XPM116 B

AbwWkWZt…kawDhufa

cddbdf1fbd8390…49aaa88cf1742f

2 in → 2 out5.0352 XPM374 B

APKpf77i…rvNzkfjn ANfPUWXD…guAbq8LZ

cdc842d2b52ef8…4806d3dcaa6e33

1 in → 2 out1.8058 XPM226 B

APQNj5oZ…3PWivVAu AcEZd46R…24AuA3Yt

7988942e017c5d…6b10e36072dfc9

2 in → 2 out5.0148 XPM375 B

AW6xKVVP…sFp5odmT AdCR6ShJ…9kwJoAbe

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.

6.132 × 10⁹⁷(98-digit number)

61323299504798036615…41171754510872198399

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

6.132 × 10⁹⁷(98-digit number)

61323299504798036615…41171754510872198399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.132 × 10⁹⁷(98-digit number)

61323299504798036615…41171754510872198401

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

1.226 × 10⁹⁸(99-digit number)

12264659900959607323…82343509021744396799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.226 × 10⁹⁸(99-digit number)

12264659900959607323…82343509021744396801

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

2.452 × 10⁹⁸(99-digit number)

24529319801919214646…64687018043488793599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.452 × 10⁹⁸(99-digit number)

24529319801919214646…64687018043488793601

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

4.905 × 10⁹⁸(99-digit number)

49058639603838429292…29374036086977587199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.905 × 10⁹⁸(99-digit number)

49058639603838429292…29374036086977587201

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

9.811 × 10⁹⁸(99-digit number)

98117279207676858585…58748072173955174399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.811 × 10⁹⁸(99-digit number)

98117279207676858585…58748072173955174401

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 #504,080

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