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Block #276,377

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/27/2013, 3:54:41 AM Β· Difficulty 9.9630 Β· 6,528,807 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
abba1709d51af0f63fde9587e9e15a4aa8f737f2605dc95f4a2d0dd67423daf0
View on Chainz β†—

Height

#276,377

Difficulty

9.963012

Transactions

1

Size

198 B

Version

2

Bits

09f687ee

Nonce

20,480

Timestamp

11/27/2013, 3:54:41 AM

Confirmations

6,528,807

Mined by

⛏️ P2SHAQVe2UA1iTQ9DYzoq3WAtRFrUDVMZmsiXq

Merkle Root

86e13cdbf261ceda9f28958249fd0cdf3b518cb45bd79a96ba8ce71260ef3077
Transactions (1)
Coinbase86e13cdbf261ce…8ce71260ef3077
1 in β†’ 1 out10.0600 XPM109 B
AQVe2UA1…VMZmsiXq
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.

1.558 Γ— 10⁹³(94-digit number)
15589019832755845162…71132096668622743079
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
1.558 Γ— 10⁹³(94-digit number)
15589019832755845162…71132096668622743079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.558 Γ— 10⁹³(94-digit number)
15589019832755845162…71132096668622743081
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
3.117 Γ— 10⁹³(94-digit number)
31178039665511690324…42264193337245486159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.117 Γ— 10⁹³(94-digit number)
31178039665511690324…42264193337245486161
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
6.235 Γ— 10⁹³(94-digit number)
62356079331023380648…84528386674490972319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.235 Γ— 10⁹³(94-digit number)
62356079331023380648…84528386674490972321
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
1.247 Γ— 10⁹⁴(95-digit number)
12471215866204676129…69056773348981944639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.247 Γ— 10⁹⁴(95-digit number)
12471215866204676129…69056773348981944641
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
2.494 Γ— 10⁹⁴(95-digit number)
24942431732409352259…38113546697963889279
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:57,685,542 XPMΒ·at block #6,805,183 Β· updates every 60s
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