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Block #86,757

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/28/2013, 9:01:33 AM Β· Difficulty 9.2868 Β· 6,709,066 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b97a08b2f8868ad4de6bd93a502f61874b36f869ff6dff4a176a4dd7fc059ffb
View on Chainz β†—

Height

#86,757

Difficulty

9.286830

Transactions

1

Size

204 B

Version

2

Bits

09496db9

Nonce

9,759

Timestamp

7/28/2013, 9:01:33 AM

Confirmations

6,709,066

Mined by

⛏️ P2SHAdhmaJ1p1gqeX3dfcHueRxnjGJMhFRDjQ7

Merkle Root

183ac7dd52ffbe352f7eef3bd6cd63310fb4d44ec9e482ac760cf7a9da195fd9
Transactions (1)
Coinbase183ac7dd52ffbe…0cf7a9da195fd9
1 in β†’ 1 out11.5800 XPM109 B
AdhmaJ1p…MhFRDjQ7
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.

2.051 Γ— 10¹⁰⁷(108-digit number)
20515961843289347740…67205033791534913749
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
2.051 Γ— 10¹⁰⁷(108-digit number)
20515961843289347740…67205033791534913749
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.051 Γ— 10¹⁰⁷(108-digit number)
20515961843289347740…67205033791534913751
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
4.103 Γ— 10¹⁰⁷(108-digit number)
41031923686578695480…34410067583069827499
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.103 Γ— 10¹⁰⁷(108-digit number)
41031923686578695480…34410067583069827501
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
8.206 Γ— 10¹⁰⁷(108-digit number)
82063847373157390960…68820135166139654999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.206 Γ— 10¹⁰⁷(108-digit number)
82063847373157390960…68820135166139655001
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
1.641 Γ— 10¹⁰⁸(109-digit number)
16412769474631478192…37640270332279309999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.641 Γ— 10¹⁰⁸(109-digit number)
16412769474631478192…37640270332279310001
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
3.282 Γ— 10¹⁰⁸(109-digit number)
32825538949262956384…75280540664558619999
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:57,610,666 XPMΒ·at block #6,795,822 Β· updates every 60s
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