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Block #85,733

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/27/2013, 3:13:12 PM Β· Difficulty 9.2931 Β· 6,716,941 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
70dc61002d30341e5ef833f7eab8619ddd99b09c46cddab2d82388244583ef2b
View on Chainz β†—

Height

#85,733

Difficulty

9.293079

Transactions

1

Size

198 B

Version

2

Bits

094b0740

Nonce

171,639

Timestamp

7/27/2013, 3:13:12 PM

Confirmations

6,716,941

Mined by

⛏️ P2SHAcqZuz9iwKJujHV847Vr8zirvaDGngwSZs

Merkle Root

f78194e6ffd5482ccb9e876404efbf219ff00b03d463556adaf06e4af61f6cb4
Transactions (1)
Coinbasef78194e6ffd548…f06e4af61f6cb4
1 in β†’ 1 out11.5600 XPM109 B
AcqZuz9i…DGngwSZs
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.

7.031 Γ— 10⁹¹(92-digit number)
70313781869422247219…26537387349512858809
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
7.031 Γ— 10⁹¹(92-digit number)
70313781869422247219…26537387349512858809
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.031 Γ— 10⁹¹(92-digit number)
70313781869422247219…26537387349512858811
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
1.406 Γ— 10⁹²(93-digit number)
14062756373884449443…53074774699025717619
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.406 Γ— 10⁹²(93-digit number)
14062756373884449443…53074774699025717621
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
2.812 Γ— 10⁹²(93-digit number)
28125512747768898887…06149549398051435239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.812 Γ— 10⁹²(93-digit number)
28125512747768898887…06149549398051435241
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
5.625 Γ— 10⁹²(93-digit number)
56251025495537797775…12299098796102870479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.625 Γ— 10⁹²(93-digit number)
56251025495537797775…12299098796102870481
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
1.125 Γ— 10⁹³(94-digit number)
11250205099107559555…24598197592205740959
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:57,665,412 XPMΒ·at block #6,802,673 Β· updates every 60s
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