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Block #273,097

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/25/2013, 3:12:54 PM Β· Difficulty 9.9541 Β· 6,543,886 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a552c74cfefdf0211238ec1f839fe9fc18665e679b7b64af3600c71f10a5cf55
View on Chainz β†—

Height

#273,097

Difficulty

9.954068

Transactions

2

Size

1.97 KB

Version

2

Bits

09f43dd5

Nonce

31,685

Timestamp

11/25/2013, 3:12:54 PM

Confirmations

6,543,886

Mined by

⛏️ P2SHARtBvc6PHD2djRoX8i8JUYCy7UpEi73FcV

Merkle Root

60e78a8eb607810ed9108a76529656d2840fe73714f327f641cb20a4ebd71dcc
Transactions (2)
Coinbase2b83f81476ee5f…8d66582793735e
1 in β†’ 1 out10.1000 XPM109 B
ARtBvc6P…pEi73FcV
575a0df8e53383…d23c1ab99e6719
12 in β†’ 1 out1.3122 XPM1.78 KB
AakCBgDN…KJzYPxJe
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.

1.834 Γ— 10⁹⁷(98-digit number)
18343755958668560377…52805726737361151999
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
1.834 Γ— 10⁹⁷(98-digit number)
18343755958668560377…52805726737361151999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.834 Γ— 10⁹⁷(98-digit number)
18343755958668560377…52805726737361152001
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
3.668 Γ— 10⁹⁷(98-digit number)
36687511917337120755…05611453474722303999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.668 Γ— 10⁹⁷(98-digit number)
36687511917337120755…05611453474722304001
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
7.337 Γ— 10⁹⁷(98-digit number)
73375023834674241511…11222906949444607999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.337 Γ— 10⁹⁷(98-digit number)
73375023834674241511…11222906949444608001
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
1.467 Γ— 10⁹⁸(99-digit number)
14675004766934848302…22445813898889215999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.467 Γ— 10⁹⁸(99-digit number)
14675004766934848302…22445813898889216001
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
2.935 Γ— 10⁹⁸(99-digit number)
29350009533869696604…44891627797778431999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.935 Γ— 10⁹⁸(99-digit number)
29350009533869696604…44891627797778432001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
5.870 Γ— 10⁹⁸(99-digit number)
58700019067739393209…89783255595556863999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,779,901 XPMΒ·at block #6,816,982 Β· updates every 60s
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