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Block #151,977

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/6/2013, 12:36:33 AM Β· Difficulty 9.8621 Β· 6,656,408 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dd8eca124f9050fbd40de3ec0257304a097e54724a0bdd4b33040a1685728661
View on Chainz β†—

Height

#151,977

Difficulty

9.862059

Transactions

2

Size

1018 B

Version

2

Bits

09dcafea

Nonce

15,654

Timestamp

9/6/2013, 12:36:33 AM

Confirmations

6,656,408

Mined by

⛏️ P2SHAP9mkN5CvZv9yJumdWwandb1esCp9EUL1P

Merkle Root

28264687756dfa5204a35c29bf9c59b39a4c1ed7e3e4c73e0ab4fee86b65b949
Transactions (2)
Coinbase22d7d34e289da8…7cfcb168bb156a
1 in β†’ 1 out10.2800 XPM109 B
AP9mkN5C…Cp9EUL1P
1b4dab86da4149…06289453111ccf
5 in β†’ 2 out563.6954 XPM819 B
AdkWAqnf…pzFM3zEAAea5qFPK…z2VFU5nR
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.964 Γ— 10⁹³(94-digit number)
79648601929604726845…02171825310311465319
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
7.964 Γ— 10⁹³(94-digit number)
79648601929604726845…02171825310311465319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.964 Γ— 10⁹³(94-digit number)
79648601929604726845…02171825310311465321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.592 Γ— 10⁹⁴(95-digit number)
15929720385920945369…04343650620622930639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.592 Γ— 10⁹⁴(95-digit number)
15929720385920945369…04343650620622930641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
3.185 Γ— 10⁹⁴(95-digit number)
31859440771841890738…08687301241245861279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.185 Γ— 10⁹⁴(95-digit number)
31859440771841890738…08687301241245861281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
6.371 Γ— 10⁹⁴(95-digit number)
63718881543683781476…17374602482491722559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.371 Γ— 10⁹⁴(95-digit number)
63718881543683781476…17374602482491722561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.274 Γ— 10⁹⁡(96-digit number)
12743776308736756295…34749204964983445119
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,711,135 XPMΒ·at block #6,808,384 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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