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Block #138,350

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/28/2013, 8:50:27 AM Β· Difficulty 9.8257 Β· 6,666,728 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
230d2c075321cba10c468339addfecc406ff319b41a5000fe644dad7651c5d7c
View on Chainz β†—

Height

#138,350

Difficulty

9.825673

Transactions

1

Size

198 B

Version

2

Bits

09d35f53

Nonce

81,281

Timestamp

8/28/2013, 8:50:27 AM

Confirmations

6,666,728

Mined by

⛏️ P2SHAeCBxDH7sDSvMYFQbBffKCJERDKR4C5bwM

Merkle Root

6022420adb3ed783373c39c3006172e86e5d4966ca299785a9d5ba58e8eecd39
Transactions (1)
Coinbase6022420adb3ed7…d5ba58e8eecd39
1 in β†’ 1 out10.3400 XPM109 B
AeCBxDH7…KR4C5bwM
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.

1.009 Γ— 10⁹³(94-digit number)
10097842666003386097…61049876276333937599
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
1.009 Γ— 10⁹³(94-digit number)
10097842666003386097…61049876276333937599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.009 Γ— 10⁹³(94-digit number)
10097842666003386097…61049876276333937601
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
2.019 Γ— 10⁹³(94-digit number)
20195685332006772195…22099752552667875199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.019 Γ— 10⁹³(94-digit number)
20195685332006772195…22099752552667875201
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
4.039 Γ— 10⁹³(94-digit number)
40391370664013544391…44199505105335750399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.039 Γ— 10⁹³(94-digit number)
40391370664013544391…44199505105335750401
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
8.078 Γ— 10⁹³(94-digit number)
80782741328027088782…88399010210671500799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.078 Γ— 10⁹³(94-digit number)
80782741328027088782…88399010210671500801
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
1.615 Γ— 10⁹⁴(95-digit number)
16156548265605417756…76798020421343001599
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:57,684,687 XPMΒ·at block #6,805,077 Β· updates every 60s
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