Block #784,276

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/26/2014, 6:44:49 PM · Difficulty 10.9751 · 6,011,316 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2db8bdbe73ab58380dbaf4cd0fd95ba80a51ad26eb666fbb20dc4ea1dd50ea31

View on Chainz ↗

Height

#784,276

Difficulty

10.975124

Transactions

Size

13.30 KB

Version

Bits

0af9a1b2

Nonce

791,738,362

Timestamp

10/26/2014, 6:44:49 PM

Confirmations

6,011,316

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

abd7dac94469ca9f44e9100a37a9d8372956b04920f457887d35ea0a7bea8eb7

Transactions (5)

Coinbase71e58c3faa25bd…99ba5c779b82c1

1 in → 1 out8.4500 XPM116 B

ANSXnLY2…Sd25TjkD

88a4e09699e6d8…8efe7dd08b1cde

1 in → 370 out2433.4346 XPM12.44 KB

AXktW6tP…i6ksHyss AXatm7Se…KGsBBnzt AXeCyy6t…caCZKmdf AXBC4B5S…LHBVkC1r AXtCwBuV…cnbwWtbY

b34d0ee7cf0f88…58923068dc442c

1 in → 2 out3.5819 XPM225 B

AKQQttQY…eEp7dvoA AGdWVjRk…LFVsqCnK

649f288ecdf79c…2ab87b57cc14ef

1 in → 2 out0.6785 XPM225 B

AMoJsji6…a13Bp22Q APAcrhs4…vc6UtScs

9916fd4942bf99…41336010f438e2

1 in → 2 out2.9275 XPM227 B

AVZwze3C…1DNKwKx6 APXpdNQN…tWfrmbJe

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.590 × 10⁹⁶(97-digit number)

25908240148579621953…41617354238753390079

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

2.590 × 10⁹⁶(97-digit number)

25908240148579621953…41617354238753390079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.590 × 10⁹⁶(97-digit number)

25908240148579621953…41617354238753390081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

5.181 × 10⁹⁶(97-digit number)

51816480297159243907…83234708477506780159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.181 × 10⁹⁶(97-digit number)

51816480297159243907…83234708477506780161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.036 × 10⁹⁷(98-digit number)

10363296059431848781…66469416955013560319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.036 × 10⁹⁷(98-digit number)

10363296059431848781…66469416955013560321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.072 × 10⁹⁷(98-digit number)

20726592118863697562…32938833910027120639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.072 × 10⁹⁷(98-digit number)

20726592118863697562…32938833910027120641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

4.145 × 10⁹⁷(98-digit number)

41453184237727395125…65877667820054241279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.145 × 10⁹⁷(98-digit number)

41453184237727395125…65877667820054241281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer