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Block #922,688

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/4/2015, 4:13:42 PM Β· Difficulty 10.9150 Β· 5,887,140 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b2a23cfdbbaa6e9582854f2bb0e5e93b804147c5b4de7d1a816754e65689d1d8
View on Chainz β†—

Height

#922,688

Difficulty

10.915022

Transactions

2

Size

4.47 KB

Version

2

Bits

0aea3ee0

Nonce

2,007,903,931

Timestamp

2/4/2015, 4:13:42 PM

Confirmations

5,887,140

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

cd7692ef481b6edfb9a1bd85c3938bff122f1680eb3968c60e0d58d6b618684e
Transactions (2)
Coinbaseb9e987e9e63a3f…920f900a6c71a0
1 in β†’ 1 out8.4300 XPM116 B
ANSXnLY2…Sd25TjkD
982880d014c33d…ab01d929801319
29 in β†’ 2 out500.0100 XPM4.27 KB
AJjnK9uC…VreFquR4AeGhVLpW…C5WKMbK8
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.

6.939 Γ— 10⁹⁡(96-digit number)
69390224100358900920…73986432469192729319
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
6.939 Γ— 10⁹⁡(96-digit number)
69390224100358900920…73986432469192729319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.939 Γ— 10⁹⁡(96-digit number)
69390224100358900920…73986432469192729321
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
1.387 Γ— 10⁹⁢(97-digit number)
13878044820071780184…47972864938385458639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.387 Γ— 10⁹⁢(97-digit number)
13878044820071780184…47972864938385458641
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
2.775 Γ— 10⁹⁢(97-digit number)
27756089640143560368…95945729876770917279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.775 Γ— 10⁹⁢(97-digit number)
27756089640143560368…95945729876770917281
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
5.551 Γ— 10⁹⁢(97-digit number)
55512179280287120736…91891459753541834559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.551 Γ— 10⁹⁢(97-digit number)
55512179280287120736…91891459753541834561
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
1.110 Γ— 10⁹⁷(98-digit number)
11102435856057424147…83782919507083669119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.110 Γ— 10⁹⁷(98-digit number)
11102435856057424147…83782919507083669121
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:57,722,709 XPMΒ·at block #6,809,827 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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