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Block #135,380

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/26/2013, 2:29:17 PM Β· Difficulty 9.8101 Β· 6,672,873 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5865b7bb7f9761b04053094ce382d060c43ef7a57e3b43caeee573392a66a2a2
View on Chainz β†—

Height

#135,380

Difficulty

9.810100

Transactions

1

Size

200 B

Version

2

Bits

09cf62b5

Nonce

478,536

Timestamp

8/26/2013, 2:29:17 PM

Confirmations

6,672,873

Mined by

⛏️ P2SHAH4jbUNYBmLJFGrDN9Kw7rxzHMQ397R4Rb

Merkle Root

f7a480df7d3554f7727816d50ea1bc239a1e405b0397e4db54a68d9a146a1afe
Transactions (1)
Coinbasef7a480df7d3554…a68d9a146a1afe
1 in β†’ 1 out10.3800 XPM109 B
AH4jbUNY…Q397R4Rb
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.

1.547 Γ— 10⁹⁷(98-digit number)
15470587375888877182…10186455637298613499
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
1.547 Γ— 10⁹⁷(98-digit number)
15470587375888877182…10186455637298613499
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.547 Γ— 10⁹⁷(98-digit number)
15470587375888877182…10186455637298613501
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
3.094 Γ— 10⁹⁷(98-digit number)
30941174751777754365…20372911274597226999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.094 Γ— 10⁹⁷(98-digit number)
30941174751777754365…20372911274597227001
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
6.188 Γ— 10⁹⁷(98-digit number)
61882349503555508730…40745822549194453999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.188 Γ— 10⁹⁷(98-digit number)
61882349503555508730…40745822549194454001
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
1.237 Γ— 10⁹⁸(99-digit number)
12376469900711101746…81491645098388907999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.237 Γ— 10⁹⁸(99-digit number)
12376469900711101746…81491645098388908001
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
2.475 Γ— 10⁹⁸(99-digit number)
24752939801422203492…62983290196777815999
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:57,710,070 XPMΒ·at block #6,808,252 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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