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Block #71,903

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/20/2013, 9:02:36 PM Β· Difficulty 8.9936 Β· 6,744,443 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
56f9b28bcbaad37cb5947df39b8269e4a4e22a2c9cb90244e83fd3414138587d
View on Chainz β†—

Height

#71,903

Difficulty

8.993627

Transactions

1

Size

202 B

Version

2

Bits

08fe5e59

Nonce

218

Timestamp

7/20/2013, 9:02:36 PM

Confirmations

6,744,443

Mined by

⛏️ P2SHAY4eujiGh7Rf2jRobCGzSZ7PJ8WpcSc51y

Merkle Root

776d6d454c907f9cf8de54398c4321e440fd70500302f8d648173374a0d7140f
Transactions (1)
Coinbase776d6d454c907f…173374a0d7140f
1 in β†’ 1 out12.3500 XPM110 B
AY4eujiG…WpcSc51y
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.

7.022 Γ— 10⁹⁹(100-digit number)
70224832051678645215…31335183387515868009
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
7.022 Γ— 10⁹⁹(100-digit number)
70224832051678645215…31335183387515868009
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.022 Γ— 10⁹⁹(100-digit number)
70224832051678645215…31335183387515868011
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
1.404 Γ— 10¹⁰⁰(101-digit number)
14044966410335729043…62670366775031736019
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.404 Γ— 10¹⁰⁰(101-digit number)
14044966410335729043…62670366775031736021
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
2.808 Γ— 10¹⁰⁰(101-digit number)
28089932820671458086…25340733550063472039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.808 Γ— 10¹⁰⁰(101-digit number)
28089932820671458086…25340733550063472041
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
5.617 Γ— 10¹⁰⁰(101-digit number)
56179865641342916172…50681467100126944079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.617 Γ— 10¹⁰⁰(101-digit number)
56179865641342916172…50681467100126944081
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
1.123 Γ— 10¹⁰¹(102-digit number)
11235973128268583234…01362934200253888159
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:57,774,892 XPMΒ·at block #6,816,345 Β· updates every 60s
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