Block #260,209

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/14/2013, 2:29:44 AM · Difficulty 9.9777 · 6,535,952 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1824f7c00baa9d79724acf73441cdb82792163df9087026cc89f06cff5614bdb

View on Chainz ↗

Height

#260,209

Difficulty

9.977748

Transactions

Size

1.36 KB

Version

Bits

09fa4db2

Nonce

589

Timestamp

11/14/2013, 2:29:44 AM

Confirmations

6,535,952

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

837fa8f157c4a346df491940264cb65ef01795fe4f34d917fa3941a10d4979e6

Transactions (5)

Coinbase81f87d3d0f01da…acde0a89c0cd9b

1 in → 2 out10.0700 XPM137 B

AZDUEbdS…RYKMRZET ALfEGCwh…VawujfMm

a36fd02eb05088…8296748fcb366c

1 in → 1 out112.0000 XPM193 B

ATPM2yfs…AQmg5mid

a06b0b558d6508…2baab5ed47a47a

3 in → 2 out150.0141 XPM521 B

AenzMFL2…WaQVnL5Z AVsAaDmq…mEme4wXb

94acb2997e9342…0448fd7bdebd5f

1 in → 2 out7.9576 XPM226 B

AciLmAhg…i3FFtyyP ANa8HV8X…KofXkhL7

600d8318464806…eb870e72a1efe8

1 in → 2 out2.9840 XPM226 B

AWnQNQXp…DPk6BRJt AaVFHFSq…bCnX1Bpw

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.

5.168 × 10⁹⁵(96-digit number)

51681860484903801630…79898668920065502239

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

5.168 × 10⁹⁵(96-digit number)

51681860484903801630…79898668920065502239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.168 × 10⁹⁵(96-digit number)

51681860484903801630…79898668920065502241

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

1.033 × 10⁹⁶(97-digit number)

10336372096980760326…59797337840131004479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.033 × 10⁹⁶(97-digit number)

10336372096980760326…59797337840131004481

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

2.067 × 10⁹⁶(97-digit number)

20672744193961520652…19594675680262008959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.067 × 10⁹⁶(97-digit number)

20672744193961520652…19594675680262008961

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

4.134 × 10⁹⁶(97-digit number)

41345488387923041304…39189351360524017919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.134 × 10⁹⁶(97-digit number)

41345488387923041304…39189351360524017921

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

8.269 × 10⁹⁶(97-digit number)

82690976775846082609…78378702721048035839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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