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Block #307,009

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/12/2013, 8:53:49 AM Β· Difficulty 9.9940 Β· 6,491,671 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
271b921a813938395c90b99fcc52a6dfb479cf9c3a0b10fefefc9c01e023bb30
View on Chainz β†—

Height

#307,009

Difficulty

9.994048

Transactions

2

Size

2.86 KB

Version

2

Bits

09fe79f3

Nonce

124,676

Timestamp

12/12/2013, 8:53:49 AM

Confirmations

6,491,671

Mined by

⛏️ AaRy3AbMAHMS8edmSw9jhkJ2fCCZzvKMwEzMSoj

Merkle Root

0a395cbdd71138064824a26b834863fbd0225ad550c87fe860ee1504ffa5b012
Transactions (2)
Coinbase837c5d1be24331…d923ba66a00885
1 in β†’ 1 out10.0000 XPM97 B
AbMAHMS8…MwEzMSoj
5931ca50db6718…0ff0f7ea7383dd
18 in β†’ 2 out7.4977 XPM2.67 KB
AUzE7bsG…5vpsuuaEAKm3LPG5…NzCYgpkx
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.

1.525 Γ— 10⁹⁹(100-digit number)
15253237325359185436…90916617466705817599
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
1.525 Γ— 10⁹⁹(100-digit number)
15253237325359185436…90916617466705817599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.525 Γ— 10⁹⁹(100-digit number)
15253237325359185436…90916617466705817601
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
3.050 Γ— 10⁹⁹(100-digit number)
30506474650718370872…81833234933411635199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.050 Γ— 10⁹⁹(100-digit number)
30506474650718370872…81833234933411635201
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
6.101 Γ— 10⁹⁹(100-digit number)
61012949301436741745…63666469866823270399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.101 Γ— 10⁹⁹(100-digit number)
61012949301436741745…63666469866823270401
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
1.220 Γ— 10¹⁰⁰(101-digit number)
12202589860287348349…27332939733646540799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.220 Γ— 10¹⁰⁰(101-digit number)
12202589860287348349…27332939733646540801
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
2.440 Γ— 10¹⁰⁰(101-digit number)
24405179720574696698…54665879467293081599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.440 Γ— 10¹⁰⁰(101-digit number)
24405179720574696698…54665879467293081601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,633,467 XPMΒ·at block #6,798,679 Β· updates every 60s
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