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Block #923,612

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/5/2015, 9:51:04 AM Β· Difficulty 10.9128 Β· 5,887,259 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
167f259dd7826729c20495b97afec4afb0e0bcddf7ad23d1c278385551acc821
View on Chainz β†—

Height

#923,612

Difficulty

10.912767

Transactions

2

Size

694 B

Version

2

Bits

0ae9ab19

Nonce

1,728,015,530

Timestamp

2/5/2015, 9:51:04 AM

Confirmations

5,887,259

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f7cf4249c503df943fa6e9ace5185af1a7409f74244233fd56eed8b141165553
Transactions (2)
Coinbasef4d358a7829c00…e171b89a34de9b
1 in β†’ 1 out8.3900 XPM116 B
ANSXnLY2…Sd25TjkD
8243a625e33195…c7520368db3bff
3 in β†’ 1 out19.7254 XPM488 B
AWF4rtPp…LnbQHVaN
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.

1.962 Γ— 10⁹⁴(95-digit number)
19628767561594684713…24592713104700984139
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
1.962 Γ— 10⁹⁴(95-digit number)
19628767561594684713…24592713104700984139
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.962 Γ— 10⁹⁴(95-digit number)
19628767561594684713…24592713104700984141
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
3.925 Γ— 10⁹⁴(95-digit number)
39257535123189369427…49185426209401968279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.925 Γ— 10⁹⁴(95-digit number)
39257535123189369427…49185426209401968281
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
7.851 Γ— 10⁹⁴(95-digit number)
78515070246378738854…98370852418803936559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.851 Γ— 10⁹⁴(95-digit number)
78515070246378738854…98370852418803936561
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
1.570 Γ— 10⁹⁡(96-digit number)
15703014049275747770…96741704837607873119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.570 Γ— 10⁹⁡(96-digit number)
15703014049275747770…96741704837607873121
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
3.140 Γ— 10⁹⁡(96-digit number)
31406028098551495541…93483409675215746239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.140 Γ— 10⁹⁡(96-digit number)
31406028098551495541…93483409675215746241
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:57,731,066 XPMΒ·at block #6,810,870 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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