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Block #30,327

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 6:39:39 PM Β· Difficulty 7.9866 Β· 6,770,261 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9b9ac2d33fdf876cb95029d18f636bd8f81dd69199adae7867695b2b486d570b
View on Chainz β†—

Height

#30,327

Difficulty

7.986645

Transactions

1

Size

197 B

Version

2

Bits

07fc94bd

Nonce

1,072

Timestamp

7/13/2013, 6:39:39 PM

Confirmations

6,770,261

Mined by

⛏️ P2SHAKSwr9eUsXtYAeGKZ6MmF96jvsdLNxuVyn

Merkle Root

a9f608def094287f9f97942ab16c2c4ee7ab6e45763714aff79febfac6a968b5
Transactions (1)
Coinbasea9f608def09428…9febfac6a968b5
1 in β†’ 1 out15.6600 XPM108 B
AKSwr9eU…dLNxuVyn
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.

1.587 Γ— 10⁹³(94-digit number)
15873601723924106271…07151838593291413239
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
1.587 Γ— 10⁹³(94-digit number)
15873601723924106271…07151838593291413239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.587 Γ— 10⁹³(94-digit number)
15873601723924106271…07151838593291413241
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
3.174 Γ— 10⁹³(94-digit number)
31747203447848212542…14303677186582826479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.174 Γ— 10⁹³(94-digit number)
31747203447848212542…14303677186582826481
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
6.349 Γ— 10⁹³(94-digit number)
63494406895696425084…28607354373165652959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.349 Γ— 10⁹³(94-digit number)
63494406895696425084…28607354373165652961
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
1.269 Γ— 10⁹⁴(95-digit number)
12698881379139285016…57214708746331305919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.269 Γ— 10⁹⁴(95-digit number)
12698881379139285016…57214708746331305921
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:57,648,762 XPMΒ·at block #6,800,587 Β· updates every 60s
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