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Block #60,719

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/18/2013, 9:30:16 AM Β· Difficulty 8.9704 Β· 6,753,669 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7884b61a194aaf1d1d21fdd8ac1bafbf91f1f7ba927bca2925e6bacf6d3f1c7d
View on Chainz β†—

Height

#60,719

Difficulty

8.970354

Transactions

1

Size

198 B

Version

2

Bits

08f86919

Nonce

28

Timestamp

7/18/2013, 9:30:16 AM

Confirmations

6,753,669

Mined by

⛏️ P2SHAKsLKPc8KMAFsNueJDJSs3dfp1zkBgUqcr

Merkle Root

c2342ec4d62a06d7d3c9e38be3f02907f6c2b7b9e9834aa86659bfa73443b97f
Transactions (1)
Coinbasec2342ec4d62a06…59bfa73443b97f
1 in β†’ 1 out12.4100 XPM110 B
AKsLKPc8…zkBgUqcr
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.

7.576 Γ— 10⁸⁸(89-digit number)
75762976108501068060…17188314073985704239
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
7.576 Γ— 10⁸⁸(89-digit number)
75762976108501068060…17188314073985704239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.576 Γ— 10⁸⁸(89-digit number)
75762976108501068060…17188314073985704241
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
1.515 Γ— 10⁸⁹(90-digit number)
15152595221700213612…34376628147971408479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.515 Γ— 10⁸⁹(90-digit number)
15152595221700213612…34376628147971408481
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
3.030 Γ— 10⁸⁹(90-digit number)
30305190443400427224…68753256295942816959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.030 Γ— 10⁸⁹(90-digit number)
30305190443400427224…68753256295942816961
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
6.061 Γ— 10⁸⁹(90-digit number)
60610380886800854448…37506512591885633919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.061 Γ— 10⁸⁹(90-digit number)
60610380886800854448…37506512591885633921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,759,165 XPMΒ·at block #6,814,387 Β· updates every 60s
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