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Block #85,305

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/27/2013, 8:52:25 AM Β· Difficulty 9.2864 Β· 6,710,980 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5fc54da7582153a1e91094d4dc396f84d5166531bba0292eb9850457c1f7cd0f
View on Chainz β†—

Height

#85,305

Difficulty

9.286380

Transactions

1

Size

203 B

Version

2

Bits

09495033

Nonce

163,864

Timestamp

7/27/2013, 8:52:25 AM

Confirmations

6,710,980

Mined by

⛏️ P2SHAdhmaJ1p1gqeX3dfcHueRxnjGJMhFRDjQ7

Merkle Root

26914b4c74839b5b44a0aedb6687c067c7cd02b89a60b16f6e8744f0a69238f9
Transactions (1)
Coinbase26914b4c74839b…8744f0a69238f9
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.

3.346 Γ— 10¹⁰³(104-digit number)
33463369813706805862…95058602556137481699
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
3.346 Γ— 10¹⁰³(104-digit number)
33463369813706805862…95058602556137481699
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.346 Γ— 10¹⁰³(104-digit number)
33463369813706805862…95058602556137481701
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
6.692 Γ— 10¹⁰³(104-digit number)
66926739627413611724…90117205112274963399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.692 Γ— 10¹⁰³(104-digit number)
66926739627413611724…90117205112274963401
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
1.338 Γ— 10¹⁰⁴(105-digit number)
13385347925482722344…80234410224549926799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.338 Γ— 10¹⁰⁴(105-digit number)
13385347925482722344…80234410224549926801
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
2.677 Γ— 10¹⁰⁴(105-digit number)
26770695850965444689…60468820449099853599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.677 Γ— 10¹⁰⁴(105-digit number)
26770695850965444689…60468820449099853601
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
5.354 Γ— 10¹⁰⁴(105-digit number)
53541391701930889379…20937640898199707199
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:57,614,283 XPMΒ·at block #6,796,284 Β· updates every 60s
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