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Block #60,269

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/18/2013, 7:02:01 AM Β· Difficulty 8.9685 Β· 6,734,185 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e6fd238e01f47e09f86943c13a50f8ecfbc2ea35ca8bd31581f100cd4cf063b6
View on Chainz β†—

Height

#60,269

Difficulty

8.968510

Transactions

1

Size

204 B

Version

2

Bits

08f7f04b

Nonce

1,164

Timestamp

7/18/2013, 7:02:01 AM

Confirmations

6,734,185

Mined by

⛏️ P2SHAa4ciwLfjjCE71yK2hN9zxTDE59b1awN3v

Merkle Root

a7a174c9ab02fd6362ffae8f166b5786f172b7083a325a8550c872bd4a8cf353
Transactions (1)
Coinbasea7a174c9ab02fd…c872bd4a8cf353
1 in β†’ 1 out12.4200 XPM110 B
Aa4ciwLf…9b1awN3v
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.

8.529 Γ— 10¹⁰⁴(105-digit number)
85293773687318283385…88330964118950560069
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
8.529 Γ— 10¹⁰⁴(105-digit number)
85293773687318283385…88330964118950560069
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.529 Γ— 10¹⁰⁴(105-digit number)
85293773687318283385…88330964118950560071
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
1.705 Γ— 10¹⁰⁡(106-digit number)
17058754737463656677…76661928237901120139
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.705 Γ— 10¹⁰⁡(106-digit number)
17058754737463656677…76661928237901120141
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
3.411 Γ— 10¹⁰⁡(106-digit number)
34117509474927313354…53323856475802240279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.411 Γ— 10¹⁰⁡(106-digit number)
34117509474927313354…53323856475802240281
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
6.823 Γ— 10¹⁰⁡(106-digit number)
68235018949854626708…06647712951604480559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.823 Γ— 10¹⁰⁡(106-digit number)
68235018949854626708…06647712951604480561
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
1.364 Γ— 10¹⁰⁢(107-digit number)
13647003789970925341…13295425903208961119
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:57,599,672 XPMΒ·at block #6,794,453 Β· updates every 60s
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