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Block #956,292

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/28/2015, 11:05:46 PM Β· Difficulty 10.8902 Β· 5,847,240 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4057b0141eb965f86e5c005defc10027660ee1cbf5c4c2700e2b078e6024068f
View on Chainz β†—

Height

#956,292

Difficulty

10.890237

Transactions

2

Size

434 B

Version

2

Bits

0ae3e68e

Nonce

137,558,677

Timestamp

2/28/2015, 11:05:46 PM

Confirmations

5,847,240

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

9b17c369d13187d2d44283de5ffd4f0492b0cc9590b3bfa3edbe8961b2956772
Transactions (2)
Coinbase05d788210befd6…335eb76648b2d7
1 in β†’ 1 out8.4300 XPM116 B
ANSXnLY2…Sd25TjkD
ebcc743a3089ce…54ba2b25eacfa0
1 in β†’ 2 out7.7704 XPM227 B
AYVZjMse…kRxkvq49Ab5uypEx…mVqX8FmY
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.

5.639 Γ— 10⁹⁢(97-digit number)
56391033757802659683…77147168429387135999
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
5.639 Γ— 10⁹⁢(97-digit number)
56391033757802659683…77147168429387135999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.639 Γ— 10⁹⁢(97-digit number)
56391033757802659683…77147168429387136001
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
1.127 Γ— 10⁹⁷(98-digit number)
11278206751560531936…54294336858774271999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.127 Γ— 10⁹⁷(98-digit number)
11278206751560531936…54294336858774272001
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
2.255 Γ— 10⁹⁷(98-digit number)
22556413503121063873…08588673717548543999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.255 Γ— 10⁹⁷(98-digit number)
22556413503121063873…08588673717548544001
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
4.511 Γ— 10⁹⁷(98-digit number)
45112827006242127746…17177347435097087999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.511 Γ— 10⁹⁷(98-digit number)
45112827006242127746…17177347435097088001
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
9.022 Γ— 10⁹⁷(98-digit number)
90225654012484255492…34354694870194175999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.022 Γ— 10⁹⁷(98-digit number)
90225654012484255492…34354694870194176001
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
1.804 Γ— 10⁹⁸(99-digit number)
18045130802496851098…68709389740388351999
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:57,672,284 XPMΒ·at block #6,803,531 Β· updates every 60s
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